On (co-)morphisms of $n$-Lie-Rinehart algebras with applications to Nambu-Poisson manifolds

TL;DR

This paper unifies the understanding of morphisms and comorphisms of $n$-Lie-Rinehart algebras and establishes their relation to Nambu-Poisson manifolds, revealing categorical equivalences and algebraic structures.

Contribution

It introduces a unified framework for morphisms and comorphisms of $n$-Lie-Rinehart algebras and relates them to Nambu-Poisson structures and $n$-Lie algebroids.

Findings

Morphisms and comorphisms form subalgebras of the $$-sum.

Category of vector bundles with Nambu-Poisson structures is equivalent to dual bundles with $n$-Lie algebroid structures.

Unified description of morphisms and comorphisms for $n$-Lie-Rinehart algebras and algebroids.

Abstract

In this paper, we give a unified description of morphisms and comorphisms of $n$-Lie-Rinehart algebras. We show that these morphisms and comorphisms can be regarded as two subalgebras of the $\psi$-sum of $n$-Lie-Rinehart algebras. We also provide similar descriptions for morphisms and comorphisms of $n$-Lie algebroids. It is proved that the category of vector bundles with Nambu-Poisson structures of rank $n$ and the category of their dual bundles with $n$-Lie algebroid structures of rank $n$ are equivalent to each other.